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YCor
YCor
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Discrete Central Subgroupcentral subgroup of a Connectedconnected Lie Groupgroup is Finitely Generatedfinitely generated

Every discrete central subgroup of a connected Lie group is finitely generated.

This result was alluded to without comment in a book I was reading (Lie Group Actions in Complex Analysis by D. Akhiezer Proposition on page 38).

Assuming it was a trivial result, I posted to math.stackexchange where YCor was kind enough to give the not so trivial reference: http://www.normalesup.org/~cornulier/MetricLC.pdf Corollary 8.A.23 here.

That Corollary uses a handful of results + definitions that are not so familiar to me and would take up some time to understand.

So before I begin going through the reference, I wanted to see if someone knew of a more concise/elementary proof of this result.

Note: I am aware that the case where the center of the Lie Group has finitely many components is exercise level.

Thanks.

Discrete Central Subgroup of a Connected Lie Group is Finitely Generated

This result was alluded to without comment in a book I was reading (Lie Group Actions in Complex Analysis by D. Akhiezer Proposition on page 38).

Assuming it was a trivial result, I posted to math.stackexchange where YCor was kind enough to give the not so trivial reference: http://www.normalesup.org/~cornulier/MetricLC.pdf Corollary 8.A.23.

That Corollary uses a handful of results + definitions that are not so familiar to me and would take up some time to understand.

So before I begin going through the reference, I wanted to see if someone knew of a more concise/elementary proof of this result.

Note: I am aware that the case where the center of the Lie Group has finitely many components is exercise level.

Thanks.

Discrete central subgroup of a connected Lie group is finitely generated

Every discrete central subgroup of a connected Lie group is finitely generated.

This result was alluded to without comment in a book I was reading (Lie Group Actions in Complex Analysis by D. Akhiezer Proposition on page 38).

Assuming it was a trivial result, I posted to math.stackexchange where YCor was kind enough to give the not so trivial reference: Corollary 8.A.23 here.

That Corollary uses a handful of results + definitions that are not so familiar to me and would take up some time to understand.

So before I begin going through the reference, I wanted to see if someone knew of a more concise/elementary proof of this result.

Note: I am aware that the case where the center of the Lie Group has finitely many components is exercise level.

Thanks.

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Calamardo
Calamardo
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Discrete Central Subgroup of a Connected Lie Group is Finitely Generated

This result was alluded to without comment in a book I was reading (Lie Group Actions in Complex Analysis by D. Akhiezer Proposition on page 38).

Assuming it was a trivial result, I posted to math.stackexchange where YCor was kind enough to give the not so trivial reference: http://www.normalesup.org/~cornulier/MetricLC.pdf Corollary 8.A.23.

That Corollary uses a handful of results + definitions that are not so familiar to me and would take up some time to understand.

So before I begin going through the reference, I wanted to see if someone knew of a more concise/elementary proof of this result.

Note: I am aware that the case where the center of the Lie Group has finitely many components is exercise level.

Thanks.